The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately t $o _____$ m/s.
Options

Question

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately t $o _____$ m/s.

Options

G1 Physics · Accepted Answer

For a longitudinal wave in a solid bar, v = √(Y/ρ). For small changes, Δv/v = ½(ΔY/Y - Δρ/ρ). Given, ΔY/Y = +1%, Δρ/ρ = +0.5%. Therefore, Δv/v = ½(1%-0.5%) = 0.25%. Hence, Δv = 0.25% of 400 = 0.0025×400 = 1 m/s. Therefore, v(final) = 400+1 = 401 m/s. Correct option: D.

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately t o _____ m/s.